In this paper, we study the following generalized quasilinear Schrodinger equa- tions with critical or supercritical growths-div（g2（u）△u） ＋ g（u）g＇（u）｜△u｜2 ＋ V（x）u = f（x, u） ＋ λ｜u｜P-2 u, x ∈ RN,...In this paper, we study the following generalized quasilinear Schrodinger equa- tions with critical or supercritical growths-div（g2（u）△u） ＋ g（u）g＇（u）｜△u｜2 ＋ V（x）u = f（x, u） ＋ λ｜u｜P-2 u, x ∈ RN,where λ 〉 0, N ≥ 3, g ： R →R＋ is a C1 even function, g（0） = 1, g＇（s） ≥ 0 for all s ≥ 0, lim ｜s｜→＋ ∞g（s）/｜s｜α-1：= β 〉 0 for some α≥ 1 and （α- 1）g（s） 〉 g＇（s）s for all s 〉 0 and p≥α2＊.Under some suitable conditions, we prove that the equation has a nontrivial solution for smallλ 〉 0 using a change of variables and variational method.展开更多
The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show tha...The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.展开更多
In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous ...In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.展开更多
This paper investigates a technique of retrieving three-dimensional windfields from the dual-Doppler weather radar radial wind which is based on the Cartesian space usingvariational method. This technology provides a ...This paper investigates a technique of retrieving three-dimensional windfields from the dual-Doppler weather radar radial wind which is based on the Cartesian space usingvariational method. This technology provides a simultaneous resolution of three wind components andsatisfies both the minimal dual-equation system and the continuity equation. The main advantage ofthis method is that it can remove the potential drawback of an iterative solution of Cartesiandual-Doppler analysis techniques which is a major demerit when one retrieves the vertical velocityusing mass continuity equation with iterative method. The data pre-processing technology andinterpolation are also studied. This work developed a three-dimensional Cressman weighting functionto process the interpolation. In order to test the capability and advantage of this method, onenumerical experiment based on simulating dual-Doppler radar observations is designed. Firstly, wesynthesize the dual-Doppler radar radial velocity and reflectivity from the numerical model. Then,the three-dimensional wind components are retrieved from the radial velocity and reflectivity usingthis technique. The retrieved three-dimensional wind fields are found to be quite consisted withthose previously simulated wind fields. Mean difference, root-mean-square error, and relativedeviation are defined to test the precision of the method. These statistic errors reveal theaccuracy and the advantage of this method. The numerical experiment has definitely testified thatthis technique can be used to retrieve the three-dimensional wind fields from the radial velocityand reflectivity detected by the real dual-Doppler weather radar.展开更多
基金supported in part by the National Natural Science Foundation of China(1150140311461023)the Shanxi Province Science Foundation for Youths under grant 2013021001-3
文摘In this paper, we study the following generalized quasilinear Schrodinger equa- tions with critical or supercritical growths-div（g2（u）△u） ＋ g（u）g＇（u）｜△u｜2 ＋ V（x）u = f（x, u） ＋ λ｜u｜P-2 u, x ∈ RN,where λ 〉 0, N ≥ 3, g ： R →R＋ is a C1 even function, g（0） = 1, g＇（s） ≥ 0 for all s ≥ 0, lim ｜s｜→＋ ∞g（s）/｜s｜α-1：= β 〉 0 for some α≥ 1 and （α- 1）g（s） 〉 g＇（s）s for all s 〉 0 and p≥α2＊.Under some suitable conditions, we prove that the equation has a nontrivial solution for smallλ 〉 0 using a change of variables and variational method.
基金supported by the National Natural Science Foundation of China (No.10772103)the Shanghai Leading Academic Discipline Project (No.Y0103)
文摘The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.
基金supported by the National Natural Science Foundation of China(11326139,11326145)Tian Yuan Foundation(KJLD12067)+1 种基金Central Specialized Fundation of SCUEC(CZQ13013)the Project of Jiangxi Province Technology Hall(2014BAB211010)
文摘In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.
基金This work is supported by the National Key Basic Research and Development Project of China (2004CB418305), by the NationalNatural Science Foundation of China under Grant No. 40375006, and by the project of Ministry of Science and Technology ofChina (2002
文摘This paper investigates a technique of retrieving three-dimensional windfields from the dual-Doppler weather radar radial wind which is based on the Cartesian space usingvariational method. This technology provides a simultaneous resolution of three wind components andsatisfies both the minimal dual-equation system and the continuity equation. The main advantage ofthis method is that it can remove the potential drawback of an iterative solution of Cartesiandual-Doppler analysis techniques which is a major demerit when one retrieves the vertical velocityusing mass continuity equation with iterative method. The data pre-processing technology andinterpolation are also studied. This work developed a three-dimensional Cressman weighting functionto process the interpolation. In order to test the capability and advantage of this method, onenumerical experiment based on simulating dual-Doppler radar observations is designed. Firstly, wesynthesize the dual-Doppler radar radial velocity and reflectivity from the numerical model. Then,the three-dimensional wind components are retrieved from the radial velocity and reflectivity usingthis technique. The retrieved three-dimensional wind fields are found to be quite consisted withthose previously simulated wind fields. Mean difference, root-mean-square error, and relativedeviation are defined to test the precision of the method. These statistic errors reveal theaccuracy and the advantage of this method. The numerical experiment has definitely testified thatthis technique can be used to retrieve the three-dimensional wind fields from the radial velocityand reflectivity detected by the real dual-Doppler weather radar.
